math problem?

Question

ok my teacher wants us to figure out how a boy a hundred years ago got the solution to this problem in few seconds
the problem goes. whatr is the solution of all the NATURAL numbers added together. thas 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15..........+100
(you add all the numbers from 1 to 100 together, and get the solution in a fast way)
ps. if you can give the the solution to the addition

Answer 1

The boy a hundred years ago was named Gauss, who was quite the popular mathematician.

The solution is n(n+1)/2, where n is the last number.

For the case of n = 100, the sum is
S = 100(100+1)/2 = 50(101) = 5050

Answer 2

The boy simply saw that lower numbers could quickly be added to the highest numbers to =100. For example, 1+99=100, 2+98=100, etc. If you were to keep on going like this, you would add all the lowest to the highest in order and have to stop at 50 because it's the only number left. So now you have 49 equations all equaling 100, so that's 4900, then add the remaining 50. The answer is 4950, then add the 100, giving you the final answer of 5050.

Answer 3

The answer would be 5050. THis works because 1+99 = 100 and 2+98 = 100 and you do this all the way.. and this gives you 4900 and then 50 and 100 are left out so you add them out to get a total of 5050.

Answer 4

1+ 99 = 100
2 + 98 = 100
3 + 97 = 100
↓ ↓ ↓ ↓
49+ 51= 100
Plus the final 100 and the 50 in the centre.
(100*49) + 100 + 50 = 5050

Answer 5

n(n+1)/2=100*101/2=5050